`6i^(50) + 5i^(33) - 2i^(15) + 6i^(48) = 7i`.

Prove that: (i) 1+i^(2)+i^(4)+i^(6)=0 (ii) 1+i^(10)+i^(100)+i^(1000)=2 (iii) i^(104)+i^(109)+i^(114)+i^(119)=0 (iv) 6i^(54)+5i^(37)-2i^(11)+6i^(68)=7i (v) (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+i^(580)+i^(578)+i^(576)+i^(574))=-1

Show that 6i^(50)+5i^(17)-i^(11)+6i^(28) is an imaginary number.

Show that 6i^(50)+5i^(17)-i^(11)+6i^(28) is an imaginary number.

Find the value of i^(4) + i^(5) + i^(6) + i^(7) .

Evaluate 2i^(2)+ 6i^(3)+3i^(16) -6i^(19) + 4i^(25)

Evaluate 2i^(2)+ 6i^(3)+3i^(16) -6i^(19) + 4i^(25)

Write the following in the form x+iy: (i) (3+2i)(2-i) (ii) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25) . (iii) ((3-2i)(2+3i))/((1+2i)(2-i)) .

Prove that: (i) (1-i)^(2)=-2i (ii) (1+i)^(4)xx(1+(1)/(i))^(4)=16 (iii) {i^(19)+((1)/(i))^(25)}^(2)=-4 (iv) i^(4n)+i^(4n+1)+i^(4n+2)+i^(4n+3)=0 (v) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25)=1+4i .

Prove that : 6i^54+5i^37-2i^11+6i^68=7i .

Show that ((19- 7i)/(9 + i))^(12) + ((20 - 5i)/(7 - 6i))^(12) is real.